
where \(X = - \frac{1}{2} \partial ^{\mu }\phi \partial _{\mu }\phi \) , with
\(V(\phi )\)  being the potential function for the inflaton and \(f(\phi )\) 
is the redefined warp factor. The form for the warp factor function
can be phenomenologicaly deformed depending on the desired model
construction. For the well-studied AdS
throat [1]}, [2]} the warp factor
function is given by \(f(\phi ) = {f_{0}}/{\phi ^{4}}\)  with \(f_{0}\)  being
a positive constant. For definiteness, this is the form for the
warp factor function that we will be assuming in this work.
